The present invention relates to an FIR digital filter, especially to an FIR digital filter used for filtering in pass band and for digital communications processing using multi-carrier (a plurality of subcarriers).
In the filter coefficient h(n) of a conventional linear phase FIR digital filter such as a roll off filter having characteristics as shown in Fig.3, the following equations, h(0)=h(N-1), h(1)=h(N-2) , . . . , h((N-1)/2) =h ((N+1)/2), are satisfied when N is an odd number, where N is degree of the filter coefficient, the string of h(0), h (1), h(2), . . . , h (N-2), h (N-1) is an N impulse response string (discrete time signal string of impulse response). Also, when N is an even number, h(0)=h(N-1), h(1)=h(N-2), . . . , h(N/2-1)=h(N/2+1).
Like this, it is known that these kinds of filters generally meet the equation, h(n)=h(N-1-n), where n is a natural number meeting 0&lt;n&lt;N, and have a symmetric characteristics in the impulse response string.
In addition, in FIG. 3, T is a data transmission interval, .alpha. is roll off rate and .omega. is an arbitrary frequency.
As a prior art using this symmetry characteristics of impulse response string, an digital filter shown in FIG. 4 disclosed in Japanese Patent publication No. 6691(1991).
In FIG. 4, 700 is a shift register, 701 is a coefficient storing means, 702 is a reversible counter, 703 is a control circuit, 704 is a multiplier, 705 is an adder and 706 is an accumulator.
Features of this FIR digital filter are as below.
The system function of the FIR digital filter is represented by using a complex variable z of z-transformation as below. ##EQU1## If this filter is a linear phase FIR digital filter of which impulse response satisfies h(n)=h(N-1-n), coefficient data corresponding to h(0) to h((N-1)/2) are stored in the coefficient storing circuit 701 when the filter degree N is an odd number, or coefficient data corresponding to h(0) to h(N/2-1) are stored in the coefficient storing circuit 701 when the filter degree N is an even number.
Next, when the filter degree N is an odd number, the reversible counter 702 sequentially reads the coefficient data from h(0) to h((N-1 )/2) in order of n of h(n), then reads h((N-3)/2)) to h(0) in order contrary to the previous order.
Similarly to this, when the filter degree N is an even number, the reversible counter 702 sequentially reads the coefficient data from h(0) to h(N/2-1) in order of n of h(n), then reads h(N/2-1) to h(0) in order contrary to the previous order.
Next, the coefficient data read as above and input data stored in the shift register 700 are multiplied in the multiplier 704 and supplied to the adder 705, and a result of sum of products operation is output from the accumulator 706.
As described above, an FIR digital filter of which storage capacity is a half for N impulse response string h(0) to h(N-1) is offered.
Moreover, as an FIR digital filter using symmetry characteristics of impulse response string, there is an FIR digital filter disclosed in Japanese Patent Laid-Open No. 38005(1992).
This filter is an FIR filter having 2N taps symmetric coefficients. In this FIR digital filter, 1, 2, 3, . . . , N delayed input data are stored in the first RAM and N+1, N+2, N+3, . . . , 2N delayed input data are stored in the second RAM, respectively. Then, a multiplier receives data in order of 1, 2, 3, . . . , N from the first RAM and in the order of 2N, 2N-1, . . . , N+1 from the second RAM, and conducts sum of products operation between them and an impulse response string, h(0) to h(N).
Like this, operation time becomes a half of that in prior art.
As related arts in this field, there are arts disclosed in Japanese Patent Laid-Open No.347921(1992), Japanese Patent Laid-Open No.332224(1992), Japanese Patent Laid-Open No.261214(1991), Japanese Patent Laid-Open No.228421(1991), Japanese Patent Laid-Open No.211910(1991), Japanese Patent Laid-Open No.78310(1991), Japanese Patent Laid-Open No.117437(1989), Japanese Patent Laid-Open No.260314(1988).
The prior FIR digital filters described above are for filtering in based band, they are limited for a case that the applied impulse response string, h(n) to h(N-1) is represented by h(n)=h(N-1-n), where n is a natural number of the range, 0&lt;n&lt;N.
For example, as shown in FIG. 5, in a case of roll off filtering in a pass band where the impulse response S(t) is represented by the equation, S(t)=H(t)exp(j.omega.t), where H(t) is roll off characteristics and .omega. is an arbitrary frequency, symmetric characteristics of impulse response string is lost. Because, the filter coefficients are represented by complex numbers and the impulse response string s(n)=a(n)+jb(n), where a(n) represents a series of real number coefficients, b(n) represents a series of imaginary number coefficients, becomes s(n).noteq.S(N-1-n) when a(n)=a(N-1-n) and b(n)=-b(N-1-n), where N is a number of degree of the filter.
Therefore,there has been a problem that, by only turning back reading out of the impulse response string from the center like in the prior FIR digital filter described above, it is impossible to delete any impulse response string stored in the coefficient storing circuits.
Moreover, as shown in FIG. 6, in case that input data is a signal consisted of two carriers located in symmetry to 0Hz frequency axis, for roll off filtering both the carrier 1 signal and the carrier 2 signal on its carrier frequency axis, impulse response S(t)s are respectively represented by the following equations, EQU S1(t)=H(t)exp(j.omega.1t) EQU S2(t)=H(t)exp(j.omega.2t)
where, H(t) is roll off characteristics, .omega.1 is frequency of the carrier 1 and .omega.2 is frequency of carrier 2.
Therefore, in configuration of a prior FIR digital filter, to store only an impulse response string having a specific filter characteristics, the impulse response S1(t), for example, in the coefficient storing circuits 701 shown in FIG. 4, processing of the carrier 1 signal and carrier 2 signal must be conducted separately, so that impulse response strings stored in the coefficient storing circuits becomes two kinds for the carrier 1 and the carrier 2. As the result, operation time becomes twice compared with that for processing a carrier consisted of single wave, reduction of circuit size, power consumption and so on has been desired.